170 (number)
| ||||
---|---|---|---|---|
Cardinal | one hundred seventy | |||
Ordinal |
170th (one hundred and seventieth) | |||
Factorization | 2 × 5 × 17 | |||
Divisors | 1, 2, 5, 10, 17, 34, 85, 170 | |||
Roman numeral | CLXX | |||
Binary | 101010102 | |||
Ternary | 200223 | |||
Quaternary | 22224 | |||
Quinary | 11405 | |||
Senary | 4426 | |||
Octal | 2528 | |||
Duodecimal | 12212 | |||
Hexadecimal | AA16 | |||
Vigesimal | 8A20 | |||
Base 36 | 4Q36 |
170 (one hundred [and] seventy) is the natural number following 169 and preceding 171.
In mathematics
170 is the smallest n for which φ(n) and σ(n) are both square(64 and 324 respectively). But 170 is never a solution for φ(x), making it a nontotient. Nor is it ever a solution to x - φ(x), making it a noncototient.
170 is a repdigit in base 4 (2222) and base 16 (AA), as well as in bases 33, 84, and 169. It is also a sphenic number.
170 is the largest integer for which its factorial can be stored in double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10306.
There are 170 different cyclic Gilbreath permutations on 12 elements,[1] and therefore there are 170 different real periodic points of order 12 on the Mandelbrot set.[2]
In sports
- 170 is the maximum check-out possible in a standard game of darts (where the final score must be a double). It consists of two treble-twenties and a double-bullseye.[3]
See also
- 170s
- E170 (disambiguation)
- F170 (disambiguation)
- List of highways numbered 170
- United States Supreme Court cases, Volume 170
- United Nations Security Council Resolution 170
- Pennsylvania House of Representatives, District 170
References
- ↑ "Sloane's A000048". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Diaconis, Persi; Graham, Ron (2012), "Chapter 5: From the Gilbreath Principle to the Mandelbrot Set", Magical Mathematics: the mathematical ideas that animate great magic tricks, Princeton University Press, pp. 61–83.
- ↑ Rushin, Steve (2007), The Caddie Was a Reindeer: And Other Tales of Extreme Recreation, Grove Press, p. 79, ISBN 9781555847333.
External links
Wikimedia Commons has media related to 170 (number). |